HONG KONG—A co-founder of the activist group at the center of threats to paralyze Hong Kong's business district with anti-Beijing protests adopted a somber tone on Tuesday, saying its goal of securing a representative voting system in the city was "close to failure."

Chan Kin-man, one of Occupy Central's co-founders, said some of its support is waning after Beijing's decision on Sunday that effectively allows China to determine who can govern Hong Kong. The group had led a pro-democracy campaign demanding popular...